Forward Amortized Inference for Likelihood-Free Variational Marginalization
This work addresses the problem of scalable and flexible Bayesian inference for researchers and practitioners in machine learning, offering a novel approach that is incremental in advancing variational inference techniques.
The paper tackles the challenge of performing variational inference without requiring evaluations of the model joint distribution or its derivatives by introducing forward amortized inference, a likelihood-free method using the forward KL divergence, and demonstrates its application in training a Bayesian forecaster for chaotic atmospheric convection and a meta-classification network that solves arbitrary classification problems without further training.
In this paper, we introduce a new form of amortized variational inference by using the forward KL divergence in a joint-contrastive variational loss. The resulting forward amortized variational inference is a likelihood-free method as its gradient can be sampled without bias and without requiring any evaluation of either the model joint distribution or its derivatives. We prove that our new variational loss is optimized by the exact posterior marginals in the fully factorized mean-field approximation, a property that is not shared with the more conventional reverse KL inference. Furthermore, we show that forward amortized inference can be easily marginalized over large families of latent variables in order to obtain a marginalized variational posterior. We consider two examples of variational marginalization. In our first example we train a Bayesian forecaster for predicting a simplified chaotic model of atmospheric convection. In the second example we train an amortized variational approximation of a Bayesian optimal classifier by marginalizing over the model space. The result is a powerful meta-classification network that can solve arbitrary classification problems without further training.